{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization Methods\n",
    "\n",
    "Until now, you've always used Gradient Descent to update the parameters and minimize the cost. In this notebook, you will learn more advanced optimization methods that can speed up learning and perhaps even get you to a better final value for the cost function. Having a good optimization algorithm can be the difference between waiting days vs. just a few hours to get a good result. \n",
    "\n",
    "Gradient descent goes \"downhill\" on a cost function $J$. Think of it as trying to do this: \n",
    "<img src=\"images/cost.jpg\" style=\"width:650px;height:300px;\">\n",
    "<caption><center> <u> **Figure 1** </u>: **Minimizing the cost is like finding the lowest point in a hilly landscape**<br> At each step of the training, you update your parameters following a certain direction to try to get to the lowest possible point. </center></caption>\n",
    "\n",
    "**Notations**: As usual, $\\frac{\\partial J}{\\partial a } = $ `da` for any variable `a`.\n",
    "\n",
    "To get started, run the following code to import the libraries you will need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jovyan/work/week6/opt_utils.py:76: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], layer_dims[l-1])\n",
      "/home/jovyan/work/week6/opt_utils.py:77: SyntaxWarning: assertion is always true, perhaps remove parentheses?\n",
      "  assert(parameters['W' + str(l)].shape == layer_dims[l], 1)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.io\n",
    "import math\n",
    "import sklearn\n",
    "import sklearn.datasets\n",
    "\n",
    "from opt_utils import load_params_and_grads, initialize_parameters, forward_propagation, backward_propagation\n",
    "from opt_utils import compute_cost, predict, predict_dec, plot_decision_boundary, load_dataset\n",
    "from testCases import *\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (7.0, 4.0) # set default size of plots\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 - Gradient Descent\n",
    "\n",
    "A simple optimization method in machine learning is gradient descent (GD). When you take gradient steps with respect to all $m$ examples on each step, it is also called Batch Gradient Descent. \n",
    "\n",
    "**Warm-up exercise**: Implement the gradient descent update rule. The  gradient descent rule is, for $l = 1, ..., L$: \n",
    "$$ W^{[l]} = W^{[l]} - \\alpha \\text{ } dW^{[l]} \\tag{1}$$\n",
    "$$ b^{[l]} = b^{[l]} - \\alpha \\text{ } db^{[l]} \\tag{2}$$\n",
    "\n",
    "where L is the number of layers and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary. Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_gd\n",
    "\n",
    "def update_parameters_with_gd(parameters, grads, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using one step of gradient descent\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters to be updated:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients to update each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "\n",
    "    # Update rule for each parameter\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l+1)] = parameters[\"W\" + str(l+1)] - learning_rate*grads[\"dW\" + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters[\"b\" + str(l+1)] - learning_rate*grads[\"db\" + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.63535156 -0.62320365 -0.53718766]\n",
      " [-1.07799357  0.85639907 -2.29470142]]\n",
      "b1 = [[ 1.74604067]\n",
      " [-0.75184921]]\n",
      "W2 = [[ 0.32171798 -0.25467393  1.46902454]\n",
      " [-2.05617317 -0.31554548 -0.3756023 ]\n",
      " [ 1.1404819  -1.09976462 -0.1612551 ]]\n",
      "b2 = [[-0.88020257]\n",
      " [ 0.02561572]\n",
      " [ 0.57539477]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, learning_rate = update_parameters_with_gd_test_case()\n",
    "\n",
    "parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63535156 -0.62320365 -0.53718766]\n",
    " [-1.07799357  0.85639907 -2.29470142]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74604067]\n",
    " [-0.75184921]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32171798 -0.25467393  1.46902454]\n",
    " [-2.05617317 -0.31554548 -0.3756023 ]\n",
    " [ 1.1404819  -1.09976462 -0.1612551 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88020257]\n",
    " [ 0.02561572]\n",
    " [ 0.57539477]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A variant of this is Stochastic Gradient Descent (SGD), which is equivalent to mini-batch gradient descent where each mini-batch has just 1 example. The update rule that you have just implemented does not change. What changes is that you would be computing gradients on just one training example at a time, rather than on the whole training set. The code examples below illustrate the difference between stochastic gradient descent and (batch) gradient descent. \n",
    "\n",
    "- **(Batch) Gradient Descent**:\n",
    "\n",
    "``` python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    # Forward propagation\n",
    "    a, caches = forward_propagation(X, parameters)\n",
    "    # Compute cost.\n",
    "    cost = compute_cost(a, Y)\n",
    "    # Backward propagation.\n",
    "    grads = backward_propagation(a, caches, parameters)\n",
    "    # Update parameters.\n",
    "    parameters = update_parameters(parameters, grads)\n",
    "        \n",
    "```\n",
    "\n",
    "- **Stochastic Gradient Descent**:\n",
    "\n",
    "```python\n",
    "X = data_input\n",
    "Y = labels\n",
    "parameters = initialize_parameters(layers_dims)\n",
    "for i in range(0, num_iterations):\n",
    "    for j in range(0, m):\n",
    "        # Forward propagation\n",
    "        a, caches = forward_propagation(X[:,j], parameters)\n",
    "        # Compute cost\n",
    "        cost = compute_cost(a, Y[:,j])\n",
    "        # Backward propagation\n",
    "        grads = backward_propagation(a, caches, parameters)\n",
    "        # Update parameters.\n",
    "        parameters = update_parameters(parameters, grads)\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Stochastic Gradient Descent, you use only 1 training example before updating the gradients. When the training set is large, SGD can be faster. But the parameters will \"oscillate\" toward the minimum rather than converge smoothly. Here is an illustration of this: \n",
    "\n",
    "<img src=\"images/kiank_sgd.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 1** </u><font color='purple'>  : **SGD vs GD**<br> \"+\" denotes a minimum of the cost. SGD leads to many oscillations to reach convergence. But each step is a lot faster to compute for SGD than for GD, as it uses only one training example (vs. the whole batch for GD). </center></caption>\n",
    "\n",
    "**Note** also that implementing SGD requires 3 for-loops in total:\n",
    "1. Over the number of iterations\n",
    "2. Over the $m$ training examples\n",
    "3. Over the layers (to update all parameters, from $(W^{[1]},b^{[1]})$ to $(W^{[L]},b^{[L]})$)\n",
    "\n",
    "In practice, you'll often get faster results if you do not use neither the whole training set, nor only one training example, to perform each update. Mini-batch gradient descent uses an intermediate number of examples for each step. With mini-batch gradient descent, you loop over the mini-batches instead of looping over individual training examples.\n",
    "\n",
    "<img src=\"images/kiank_minibatch.png\" style=\"width:750px;height:250px;\">\n",
    "<caption><center> <u> <font color='purple'> **Figure 2** </u>: <font color='purple'>  **SGD vs Mini-Batch GD**<br> \"+\" denotes a minimum of the cost. Using mini-batches in your optimization algorithm often leads to faster optimization. </center></caption>\n",
    "\n",
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- The difference between gradient descent, mini-batch gradient descent and stochastic gradient descent is the number of examples you use to perform one update step.\n",
    "- You have to tune a learning rate hyperparameter $\\alpha$.\n",
    "- With a well-turned mini-batch size, usually it outperforms either gradient descent or stochastic gradient descent (particularly when the training set is large)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 - Mini-Batch Gradient descent\n",
    "\n",
    "Let's learn how to build mini-batches from the training set (X, Y).\n",
    "\n",
    "There are two steps:\n",
    "- **Shuffle**: Create a shuffled version of the training set (X, Y) as shown below. Each column of X and Y represents a training example. Note that the random shuffling is done synchronously between X and Y. Such that after the shuffling the $i^{th}$ column of X is the example corresponding to the $i^{th}$ label in Y. The shuffling step ensures that examples will be split randomly into different mini-batches. \n",
    "\n",
    "<img src=\"images/kiank_shuffle.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "- **Partition**: Partition the shuffled (X, Y) into mini-batches of size `mini_batch_size` (here 64). Note that the number of training examples is not always divisible by `mini_batch_size`. The last mini batch might be smaller, but you don't need to worry about this. When the final mini-batch is smaller than the full `mini_batch_size`, it will look like this: \n",
    "\n",
    "<img src=\"images/kiank_partition.png\" style=\"width:550px;height:300px;\">\n",
    "\n",
    "**Exercise**: Implement `random_mini_batches`. We coded the shuffling part for you. To help you with the partitioning step, we give you the following code that selects the indexes for the $1^{st}$ and $2^{nd}$ mini-batches:\n",
    "```python\n",
    "first_mini_batch_X = shuffled_X[:, 0 : mini_batch_size]\n",
    "second_mini_batch_X = shuffled_X[:, mini_batch_size : 2 * mini_batch_size]\n",
    "...\n",
    "```\n",
    "\n",
    "Note that the last mini-batch might end up smaller than `mini_batch_size=64`. Let $\\lfloor s \\rfloor$ represents $s$ rounded down to the nearest integer (this is `math.floor(s)` in Python). If the total number of examples is not a multiple of `mini_batch_size=64` then there will be $\\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$ mini-batches with a full 64 examples, and the number of examples in the final mini-batch will be ($m-mini_\\_batch_\\_size \\times \\lfloor \\frac{m}{mini\\_batch\\_size}\\rfloor$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: random_mini_batches\n",
    "\n",
    "def random_mini_batches(X, Y, mini_batch_size = 64, seed = 0):\n",
    "    \"\"\"\n",
    "    Creates a list of random minibatches from (X, Y)\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (input size, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    mini_batch_size -- size of the mini-batches, integer\n",
    "    \n",
    "    Returns:\n",
    "    mini_batches -- list of synchronous (mini_batch_X, mini_batch_Y)\n",
    "    \"\"\"\n",
    "    \n",
    "    np.random.seed(seed)            # To make your \"random\" minibatches the same as ours\n",
    "    m = X.shape[1]                  # number of training examples\n",
    "    mini_batches = []\n",
    "        \n",
    "    # Step 1: Shuffle (X, Y)\n",
    "    permutation = list(np.random.permutation(m))\n",
    "    shuffled_X = X[:, permutation]\n",
    "    shuffled_Y = Y[:, permutation].reshape((1,m))\n",
    "\n",
    "    # Step 2: Partition (shuffled_X, shuffled_Y). Minus the end case.\n",
    "    num_complete_minibatches = math.floor(m/mini_batch_size) # number of mini batches of size mini_batch_size in your partitionning\n",
    "    for k in range(0, num_complete_minibatches):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:,k*mini_batch_size:(k+1)*mini_batch_size]\n",
    "        mini_batch_Y = shuffled_Y[:,k*mini_batch_size:(k+1)*mini_batch_size]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    # Handling the end case (last mini-batch < mini_batch_size)\n",
    "    if m % mini_batch_size != 0:\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        mini_batch_X = shuffled_X[:,m-mini_batch_size*num_complete_minibatches:m]\n",
    "        mini_batch_Y = shuffled_Y[:,m-mini_batch_size*num_complete_minibatches:m]\n",
    "        ### END CODE HERE ###\n",
    "        mini_batch = (mini_batch_X, mini_batch_Y)\n",
    "        mini_batches.append(mini_batch)\n",
    "    \n",
    "    return mini_batches"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape of the 1st mini_batch_X: (12288, 64)\n",
      "shape of the 2nd mini_batch_X: (12288, 64)\n",
      "shape of the 3rd mini_batch_X: (12288, 128)\n",
      "shape of the 1st mini_batch_Y: (1, 64)\n",
      "shape of the 2nd mini_batch_Y: (1, 64)\n",
      "shape of the 3rd mini_batch_Y: (1, 128)\n",
      "mini batch sanity check: [ 0.90085595 -0.7612069   0.2344157 ]\n"
     ]
    }
   ],
   "source": [
    "X_assess, Y_assess, mini_batch_size = random_mini_batches_test_case()\n",
    "mini_batches = random_mini_batches(X_assess, Y_assess, mini_batch_size)\n",
    "\n",
    "print (\"shape of the 1st mini_batch_X: \" + str(mini_batches[0][0].shape))\n",
    "print (\"shape of the 2nd mini_batch_X: \" + str(mini_batches[1][0].shape))\n",
    "print (\"shape of the 3rd mini_batch_X: \" + str(mini_batches[2][0].shape))\n",
    "print (\"shape of the 1st mini_batch_Y: \" + str(mini_batches[0][1].shape))\n",
    "print (\"shape of the 2nd mini_batch_Y: \" + str(mini_batches[1][1].shape)) \n",
    "print (\"shape of the 3rd mini_batch_Y: \" + str(mini_batches[2][1].shape))\n",
    "print (\"mini batch sanity check: \" + str(mini_batches[0][0][0][0:3]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:50%\"> \n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_X** </td> \n",
    "           <td > (12288, 64) </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_X** </td> \n",
    "           <td > (12288, 20) </td> \n",
    "    </tr>\n",
    "    <tr>\n",
    "    <td > **shape of the 1st mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 2nd mini_batch_Y** </td> \n",
    "           <td > (1, 64) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **shape of the 3rd mini_batch_Y** </td> \n",
    "           <td > (1, 20) </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **mini batch sanity check** </td> \n",
    "           <td > [ 0.90085595 -0.7612069   0.2344157 ] </td> \n",
    "    </tr>\n",
    "    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Shuffling and Partitioning are the two steps required to build mini-batches\n",
    "- Powers of two are often chosen to be the mini-batch size, e.g., 16, 32, 64, 128."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 - Momentum\n",
    "\n",
    "Because mini-batch gradient descent makes a parameter update after seeing just a subset of examples, the direction of the update has some variance, and so the path taken by mini-batch gradient descent will \"oscillate\" toward convergence. Using momentum can reduce these oscillations. \n",
    "\n",
    "Momentum takes into account the past gradients to smooth out the update. We will store the 'direction' of the previous gradients in the variable $v$. Formally, this will be the exponentially weighted average of the gradient on previous steps. You can also think of $v$ as the \"velocity\" of a ball rolling downhill, building up speed (and momentum) according to the direction of the gradient/slope of the hill. \n",
    "\n",
    "<img src=\"images/opt_momentum.png\" style=\"width:400px;height:250px;\">\n",
    "<caption><center> <u><font color='purple'>**Figure 3**</u><font color='purple'>: The red arrows shows the direction taken by one step of mini-batch gradient descent with momentum. The blue points show the direction of the gradient (with respect to the current mini-batch) on each step. Rather than just following the gradient, we let the gradient influence $v$ and then take a step in the direction of $v$.<br> <font color='black'> </center>\n",
    "\n",
    "\n",
    "**Exercise**: Initialize the velocity. The velocity, $v$, is a python dictionary that needs to be initialized with arrays of zeros. Its keys are the same as those in the `grads` dictionary, that is:\n",
    "for $l =1,...,L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "```\n",
    "**Note** that the iterator l starts at 0 in the for loop while the first parameters are v[\"dW1\"] and v[\"db1\"] (that's a \"one\" on the superscript). This is why we are shifting l to l+1 in the `for` loop."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_velocity\n",
    "\n",
    "def initialize_velocity(parameters):\n",
    "    \"\"\"\n",
    "    Initializes the velocity as a python dictionary with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    \n",
    "    Returns:\n",
    "    v -- python dictionary containing the current velocity.\n",
    "                    v['dW' + str(l)] = velocity of dWl\n",
    "                    v['db' + str(l)] = velocity of dbl\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    \n",
    "    # Initialize velocity\n",
    "    for l in range(L):\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_velocity_test_case()\n",
    "\n",
    "v = initialize_velocity(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with momentum. The momentum update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$ \\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta v_{dW^{[l]}} + (1 - \\beta) dW^{[l]} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha v_{dW^{[l]}}\n",
    "\\end{cases}\\tag{3}$$\n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{db^{[l]}} = \\beta v_{db^{[l]}} + (1 - \\beta) db^{[l]} \\\\\n",
    "b^{[l]} = b^{[l]} - \\alpha v_{db^{[l]}} \n",
    "\\end{cases}\\tag{4}$$\n",
    "\n",
    "where L is the number of layers, $\\beta$ is the momentum and $\\alpha$ is the learning rate. All parameters should be stored in the `parameters` dictionary.  Note that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$ (that's a \"one\" on the superscript). So you will need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_momentum\n",
    "\n",
    "def update_parameters_with_momentum(parameters, grads, v, beta, learning_rate):\n",
    "    \"\"\"\n",
    "    Update parameters using Momentum\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- python dictionary containing the current velocity:\n",
    "                    v['dW' + str(l)] = ...\n",
    "                    v['db' + str(l)] = ...\n",
    "    beta -- the momentum hyperparameter, scalar\n",
    "    learning_rate -- the learning rate, scalar\n",
    "    \n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- python dictionary containing your updated velocities\n",
    "    \"\"\"\n",
    "\n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    \n",
    "    # Momentum update for each parameter\n",
    "    for l in range(L):\n",
    "        \n",
    "        ### START CODE HERE ### (approx. 4 lines)\n",
    "        # compute velocities\n",
    "        v[\"dW\" + str(l+1)] = beta*v[\"dW\" + str(l+1)] + (1-beta)*grads[\"dW\" + str(l+1)]\n",
    "        v[\"db\" + str(l+1)] = beta*v[\"db\" + str(l+1)] + (1-beta)*grads[\"db\" + str(l+1)]\n",
    "        # update parameters\n",
    "        parameters[\"W\" + str(l+1)] = parameters['W' + str(l+1)] - learning_rate*v['dW' + str(l+1)]\n",
    "        parameters[\"b\" + str(l+1)] = parameters['b' + str(l+1)] - learning_rate*v['db' + str(l+1)]\n",
    "        ### END CODE HERE ###\n",
    "        \n",
    "    return parameters, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.62544598 -0.61290114 -0.52907334]\n",
      " [-1.07347112  0.86450677 -2.30085497]]\n",
      "b1 = [[ 1.74493465]\n",
      " [-0.76027113]]\n",
      "W2 = [[ 0.31930698 -0.24990073  1.4627996 ]\n",
      " [-2.05974396 -0.32173003 -0.38320915]\n",
      " [ 1.13444069 -1.0998786  -0.1713109 ]]\n",
      "b2 = [[-0.87809283]\n",
      " [ 0.04055394]\n",
      " [ 0.58207317]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v = update_parameters_with_momentum_test_case()\n",
    "\n",
    "parameters, v = update_parameters_with_momentum(parameters, grads, v, beta = 0.9, learning_rate = 0.01)\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:90%\"> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.62544598 -0.61290114 -0.52907334]\n",
    " [-1.07347112  0.86450677 -2.30085497]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.74493465]\n",
    " [-0.76027113]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.31930698 -0.24990073  1.4627996 ]\n",
    " [-2.05974396 -0.32173003 -0.38320915]\n",
    " [ 1.13444069 -1.0998786  -0.1713109 ]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.87809283]\n",
    " [ 0.04055394]\n",
    " [ 0.58207317]] </td> \n",
    "    </tr> \n",
    "\n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]]</td> \n",
    "    </tr> \n",
    "</table>\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Note** that:\n",
    "- The velocity is initialized with zeros. So the algorithm will take a few iterations to \"build up\" velocity and start to take bigger steps.\n",
    "- If $\\beta = 0$, then this just becomes standard gradient descent without momentum. \n",
    "\n",
    "**How do you choose $\\beta$?**\n",
    "\n",
    "- The larger the momentum $\\beta$ is, the smoother the update because the more we take the past gradients into account. But if $\\beta$ is too big, it could also smooth out the updates too much. \n",
    "- Common values for $\\beta$ range from 0.8 to 0.999. If you don't feel inclined to tune this, $\\beta = 0.9$ is often a reasonable default. \n",
    "- Tuning the optimal $\\beta$ for your model might need trying several values to see what works best in term of reducing the value of the cost function $J$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<font color='blue'>\n",
    "**What you should remember**:\n",
    "- Momentum takes past gradients into account to smooth out the steps of gradient descent. It can be applied with batch gradient descent, mini-batch gradient descent or stochastic gradient descent.\n",
    "- You have to tune a momentum hyperparameter $\\beta$ and a learning rate $\\alpha$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 - Adam\n",
    "\n",
    "Adam is one of the most effective optimization algorithms for training neural networks. It combines ideas from RMSProp (described in lecture) and Momentum. \n",
    "\n",
    "**How does Adam work?**\n",
    "1. It calculates an exponentially weighted average of past gradients, and stores it in variables $v$ (before bias correction) and $v^{corrected}$ (with bias correction). \n",
    "2. It calculates an exponentially weighted average of the squares of the past gradients, and  stores it in variables $s$ (before bias correction) and $s^{corrected}$ (with bias correction). \n",
    "3. It updates parameters in a direction based on combining information from \"1\" and \"2\".\n",
    "\n",
    "The update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{dW^{[l]}} = \\beta_1 v_{dW^{[l]}} + (1 - \\beta_1) \\frac{\\partial \\mathcal{J} }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{dW^{[l]}} = \\frac{v_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{dW^{[l]}} = \\beta_2 s_{dW^{[l]}} + (1 - \\beta_2) (\\frac{\\partial \\mathcal{J} }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{dW^{[l]}} = \\frac{s_{dW^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{dW^{[l]}}}{\\sqrt{s^{corrected}_{dW^{[l]}}} + \\varepsilon}\n",
    "\\end{cases}$$\n",
    "where:\n",
    "- t counts the number of steps taken of Adam \n",
    "- L is the number of layers\n",
    "- $\\beta_1$ and $\\beta_2$ are hyperparameters that control the two exponentially weighted averages. \n",
    "- $\\alpha$ is the learning rate\n",
    "- $\\varepsilon$ is a very small number to avoid dividing by zero\n",
    "\n",
    "As usual, we will store all parameters in the `parameters` dictionary  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: Initialize the Adam variables $v, s$ which keep track of the past information.\n",
    "\n",
    "**Instruction**: The variables $v, s$ are python dictionaries that need to be initialized with arrays of zeros. Their keys are the same as for `grads`, that is:\n",
    "for $l = 1, ..., L$:\n",
    "```python\n",
    "v[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "v[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "s[\"dW\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"W\" + str(l+1)])\n",
    "s[\"db\" + str(l+1)] = ... #(numpy array of zeros with the same shape as parameters[\"b\" + str(l+1)])\n",
    "\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: initialize_adam\n",
    "\n",
    "def initialize_adam(parameters) :\n",
    "    \"\"\"\n",
    "    Initializes v and s as two python dictionaries with:\n",
    "                - keys: \"dW1\", \"db1\", ..., \"dWL\", \"dbL\" \n",
    "                - values: numpy arrays of zeros of the same shape as the corresponding gradients/parameters.\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters.\n",
    "                    parameters[\"W\" + str(l)] = Wl\n",
    "                    parameters[\"b\" + str(l)] = bl\n",
    "    \n",
    "    Returns: \n",
    "    v -- python dictionary that will contain the exponentially weighted average of the gradient.\n",
    "                    v[\"dW\" + str(l)] = ...\n",
    "                    v[\"db\" + str(l)] = ...\n",
    "    s -- python dictionary that will contain the exponentially weighted average of the squared gradient.\n",
    "                    s[\"dW\" + str(l)] = ...\n",
    "                    s[\"db\" + str(l)] = ...\n",
    "\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2 # number of layers in the neural networks\n",
    "    v = {}\n",
    "    s = {}\n",
    "    \n",
    "    # Initialize v, s. Input: \"parameters\". Outputs: \"v, s\".\n",
    "    for l in range(L):\n",
    "    ### START CODE HERE ### (approx. 4 lines)\n",
    "        v[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        v[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "        s[\"dW\" + str(l+1)] = np.zeros(parameters['W' + str(l+1)].shape)\n",
    "        s[\"db\" + str(l+1)] = np.zeros(parameters['b' + str(l+1)].shape)\n",
    "    ### END CODE HERE ###\n",
    "    \n",
    "    return v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "v[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "v[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW1\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db1\"] = [[ 0.]\n",
      " [ 0.]]\n",
      "s[\"dW2\"] = [[ 0.  0.  0.]\n",
      " [ 0.  0.  0.]\n",
      " [ 0.  0.  0.]]\n",
      "s[\"db2\"] = [[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]]\n"
     ]
    }
   ],
   "source": [
    "parameters = initialize_adam_test_case()\n",
    "\n",
    "v, s = initialize_adam(parameters)\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table style=\"width:40%\"> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[ 0.  0.  0.]\n",
    " [ 0.  0.  0.]\n",
    " [ 0.  0.  0.]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[ 0.]\n",
    " [ 0.]\n",
    " [ 0.]] </td> \n",
    "    </tr>\n",
    "\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**:  Now, implement the parameters update with Adam. Recall the general update rule is, for $l = 1, ..., L$: \n",
    "\n",
    "$$\\begin{cases}\n",
    "v_{W^{[l]}} = \\beta_1 v_{W^{[l]}} + (1 - \\beta_1) \\frac{\\partial J }{ \\partial W^{[l]} } \\\\\n",
    "v^{corrected}_{W^{[l]}} = \\frac{v_{W^{[l]}}}{1 - (\\beta_1)^t} \\\\\n",
    "s_{W^{[l]}} = \\beta_2 s_{W^{[l]}} + (1 - \\beta_2) (\\frac{\\partial J }{\\partial W^{[l]} })^2 \\\\\n",
    "s^{corrected}_{W^{[l]}} = \\frac{s_{W^{[l]}}}{1 - (\\beta_2)^t} \\\\\n",
    "W^{[l]} = W^{[l]} - \\alpha \\frac{v^{corrected}_{W^{[l]}}}{\\sqrt{s^{corrected}_{W^{[l]}}}+\\varepsilon}\n",
    "\\end{cases}$$\n",
    "\n",
    "\n",
    "**Note** that the iterator `l` starts at 0 in the `for` loop while the first parameters are $W^{[1]}$ and $b^{[1]}$. You need to shift `l` to `l+1` when coding."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GRADED FUNCTION: update_parameters_with_adam\n",
    "\n",
    "def update_parameters_with_adam(parameters, grads, v, s, t, learning_rate=0.01,\n",
    "                                beta1=0.9, beta2=0.999, epsilon=1e-8):\n",
    "    \"\"\"\n",
    "    Update parameters using Adam\n",
    "    \n",
    "    Arguments:\n",
    "    parameters -- python dictionary containing your parameters:\n",
    "                    parameters['W' + str(l)] = Wl\n",
    "                    parameters['b' + str(l)] = bl\n",
    "    grads -- python dictionary containing your gradients for each parameters:\n",
    "                    grads['dW' + str(l)] = dWl\n",
    "                    grads['db' + str(l)] = dbl\n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    beta1 -- Exponential decay hyperparameter for the first moment estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the second moment estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    v -- Adam variable, moving average of the first gradient, python dictionary\n",
    "    s -- Adam variable, moving average of the squared gradient, python dictionary\n",
    "    \"\"\"\n",
    "    \n",
    "    L = len(parameters) // 2                 # number of layers in the neural networks\n",
    "    v_corrected = {}                         # Initializing first moment estimate, python dictionary\n",
    "    s_corrected = {}                         # Initializing second moment estimate, python dictionary\n",
    "    \n",
    "    # Perform Adam update on all parameters\n",
    "    for l in range(L):\n",
    "        # Moving average of the gradients. Inputs: \"v, grads, beta1\". Output: \"v\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v[\"dW\" + str(l + 1)] = beta1 * v[\"dW\" + str(l + 1)] + (1 - beta1) * grads['dW' + str(l + 1)]\n",
    "        v[\"db\" + str(l + 1)] = beta1 * v[\"db\" + str(l + 1)] + (1 - beta1) * grads['db' + str(l + 1)]\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected first moment estimate. Inputs: \"v, beta1, t\". Output: \"v_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        v_corrected[\"dW\" + str(l + 1)] = v[\"dW\" + str(l + 1)] / (1 - np.power(beta1, t))\n",
    "        v_corrected[\"db\" + str(l + 1)] = v[\"db\" + str(l + 1)] / (1 - np.power(beta1, t))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Moving average of the squared gradients. Inputs: \"s, grads, beta2\". Output: \"s\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s[\"dW\" + str(l + 1)] = beta2 * s[\"dW\" + str(l + 1)] + (1 - beta2) * np.power(grads['dW' + str(l + 1)], 2)\n",
    "        s[\"db\" + str(l + 1)] = beta2 * s[\"db\" + str(l + 1)] + (1 - beta2) * np.power(grads['db' + str(l + 1)], 2)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Compute bias-corrected second raw moment estimate. Inputs: \"s, beta2, t\". Output: \"s_corrected\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        s_corrected[\"dW\" + str(l + 1)] = s[\"dW\" + str(l + 1)] / (1 - np.power(beta2, t))\n",
    "        s_corrected[\"db\" + str(l + 1)] = s[\"db\" + str(l + 1)] / (1 - np.power(beta2, t))\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "        # Update parameters. Inputs: \"parameters, learning_rate, v_corrected, s_corrected, epsilon\". Output: \"parameters\".\n",
    "        ### START CODE HERE ### (approx. 2 lines)\n",
    "        parameters[\"W\" + str(l + 1)] = parameters[\"W\" + str(l + 1)] - (learning_rate * v_corrected[\"dW\" + str(l + 1)]) / (np.sqrt(s[\"dW\" + str(l + 1)]) + epsilon)\n",
    "        parameters[\"b\" + str(l + 1)] = parameters[\"b\" + str(l + 1)] - (learning_rate * v_corrected[\"db\" + str(l + 1)]) / (np.sqrt(s[\"db\" + str(l + 1)]) + epsilon)\n",
    "        ### END CODE HERE ###\n",
    "\n",
    "    return parameters, v, s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "W1 = [[ 1.79078098 -0.77819203 -0.69460736]\n",
      " [-1.23940418  0.69897202 -2.13510311]]\n",
      "b1 = [[ 1.911247  ]\n",
      " [-0.59477129]]\n",
      "W2 = [[ 0.48547457 -0.41580594  1.62854353]\n",
      " [-1.89370518 -0.15598161 -0.21761875]\n",
      " [ 1.30020503 -0.93345976 -0.00599259]]\n",
      "b2 = [[-1.04429386]\n",
      " [-0.12422189]\n",
      " [ 0.41637962]]\n",
      "v[\"dW1\"] = [[-0.11006192  0.11447237  0.09015907]\n",
      " [ 0.05024943  0.09008559 -0.06837279]]\n",
      "v[\"db1\"] = [[-0.01228902]\n",
      " [-0.09357694]]\n",
      "v[\"dW2\"] = [[-0.02678881  0.05303555 -0.06916608]\n",
      " [-0.03967535 -0.06871727 -0.08452056]\n",
      " [-0.06712461 -0.00126646 -0.11173103]]\n",
      "v[\"db2\"] = [[ 0.02344157]\n",
      " [ 0.16598022]\n",
      " [ 0.07420442]]\n",
      "s[\"dW1\"] = [[ 0.00121136  0.00131039  0.00081287]\n",
      " [ 0.0002525   0.00081154  0.00046748]]\n",
      "s[\"db1\"] = [[  1.51020075e-05]\n",
      " [  8.75664434e-04]]\n",
      "s[\"dW2\"] = [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
      " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
      " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]]\n",
      "s[\"db2\"] = [[  5.49507194e-05]\n",
      " [  2.75494327e-03]\n",
      " [  5.50629536e-04]]\n"
     ]
    }
   ],
   "source": [
    "parameters, grads, v, s = update_parameters_with_adam_test_case()\n",
    "parameters, v, s  = update_parameters_with_adam(parameters, grads, v, s, t = 2)\n",
    "\n",
    "print(\"W1 = \" + str(parameters[\"W1\"]))\n",
    "print(\"b1 = \" + str(parameters[\"b1\"]))\n",
    "print(\"W2 = \" + str(parameters[\"W2\"]))\n",
    "print(\"b2 = \" + str(parameters[\"b2\"]))\n",
    "print(\"v[\\\"dW1\\\"] = \" + str(v[\"dW1\"]))\n",
    "print(\"v[\\\"db1\\\"] = \" + str(v[\"db1\"]))\n",
    "print(\"v[\\\"dW2\\\"] = \" + str(v[\"dW2\"]))\n",
    "print(\"v[\\\"db2\\\"] = \" + str(v[\"db2\"]))\n",
    "print(\"s[\\\"dW1\\\"] = \" + str(s[\"dW1\"]))\n",
    "print(\"s[\\\"db1\\\"] = \" + str(s[\"db1\"]))\n",
    "print(\"s[\\\"dW2\\\"] = \" + str(s[\"dW2\"]))\n",
    "print(\"s[\\\"db2\\\"] = \" + str(s[\"db2\"]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Expected Output**:\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "    <td > **W1** </td> \n",
    "           <td > [[ 1.63178673 -0.61919778 -0.53561312]\n",
    " [-1.08040999  0.85796626 -2.29409733]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b1** </td> \n",
    "           <td > [[ 1.75225313]\n",
    " [-0.75376553]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **W2** </td> \n",
    "           <td > [[ 0.32648046 -0.25681174  1.46954931]\n",
    " [-2.05269934 -0.31497584 -0.37661299]\n",
    " [ 1.14121081 -1.09245036 -0.16498684]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **b2** </td> \n",
    "           <td > [[-0.88529978]\n",
    " [ 0.03477238]\n",
    " [ 0.57537385]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **v[\"dW1\"]** </td> \n",
    "           <td > [[-0.11006192  0.11447237  0.09015907]\n",
    " [ 0.05024943  0.09008559 -0.06837279]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db1\"]** </td> \n",
    "           <td > [[-0.01228902]\n",
    " [-0.09357694]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"dW2\"]** </td> \n",
    "           <td > [[-0.02678881  0.05303555 -0.06916608]\n",
    " [-0.03967535 -0.06871727 -0.08452056]\n",
    " [-0.06712461 -0.00126646 -0.11173103]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **v[\"db2\"]** </td> \n",
    "           <td > [[ 0.02344157]\n",
    " [ 0.16598022]\n",
    " [ 0.07420442]] </td> \n",
    "    </tr> \n",
    "    <tr>\n",
    "    <td > **s[\"dW1\"]** </td> \n",
    "           <td > [[ 0.00121136  0.00131039  0.00081287]\n",
    " [ 0.0002525   0.00081154  0.00046748]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db1\"]** </td> \n",
    "           <td > [[  1.51020075e-05]\n",
    " [  8.75664434e-04]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"dW2\"]** </td> \n",
    "           <td > [[  7.17640232e-05   2.81276921e-04   4.78394595e-04]\n",
    " [  1.57413361e-04   4.72206320e-04   7.14372576e-04]\n",
    " [  4.50571368e-04   1.60392066e-07   1.24838242e-03]] </td> \n",
    "    </tr> \n",
    "    \n",
    "    <tr>\n",
    "    <td > **s[\"db2\"]** </td> \n",
    "           <td > [[  5.49507194e-05]\n",
    " [  2.75494327e-03]\n",
    " [  5.50629536e-04]] </td> \n",
    "    </tr>\n",
    "</table>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You now have three working optimization algorithms (mini-batch gradient descent, Momentum, Adam). Let's implement a model with each of these optimizers and observe the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 - Model with different optimization algorithms\n",
    "\n",
    "Lets use the following \"moons\" dataset to test the different optimization methods. (The dataset is named \"moons\" because the data from each of the two classes looks a bit like a crescent-shaped moon.) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
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pOWkUwU3qEtmtJb0/fpResx/xuC68Y1OfiT+B9aMuqz234tQsEn9ZR8qqHcgq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I8dQMdp/sebcSSfp+77GZdTx1HWW/bVJ1t48JmpxMSdCuKH9ufw9AO/4HR69TYL8ux8+OZ60lJy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\nv5qYYyZ0Z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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390ae5c6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_X, train_Y = load_dataset()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have already implemented a 3-layer neural network. You will train it with: \n",
    "- Mini-batch **Gradient Descent**: it will call your function:\n",
    "    - `update_parameters_with_gd()`\n",
    "- Mini-batch **Momentum**: it will call your functions:\n",
    "    - `initialize_velocity()` and `update_parameters_with_momentum()`\n",
    "- Mini-batch **Adam**: it will call your functions:\n",
    "    - `initialize_adam()` and `update_parameters_with_adam()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model(X, Y, layers_dims, optimizer, learning_rate = 0.0007, mini_batch_size = 64, beta = 0.9,\n",
    "          beta1 = 0.9, beta2 = 0.999,  epsilon = 1e-8, num_epochs = 10000, print_cost = True):\n",
    "    \"\"\"\n",
    "    3-layer neural network model which can be run in different optimizer modes.\n",
    "    \n",
    "    Arguments:\n",
    "    X -- input data, of shape (2, number of examples)\n",
    "    Y -- true \"label\" vector (1 for blue dot / 0 for red dot), of shape (1, number of examples)\n",
    "    layers_dims -- python list, containing the size of each layer\n",
    "    learning_rate -- the learning rate, scalar.\n",
    "    mini_batch_size -- the size of a mini batch\n",
    "    beta -- Momentum hyperparameter\n",
    "    beta1 -- Exponential decay hyperparameter for the past gradients estimates \n",
    "    beta2 -- Exponential decay hyperparameter for the past squared gradients estimates \n",
    "    epsilon -- hyperparameter preventing division by zero in Adam updates\n",
    "    num_epochs -- number of epochs\n",
    "    print_cost -- True to print the cost every 1000 epochs\n",
    "\n",
    "    Returns:\n",
    "    parameters -- python dictionary containing your updated parameters \n",
    "    \"\"\"\n",
    "\n",
    "    L = len(layers_dims)             # number of layers in the neural networks\n",
    "    costs = []                       # to keep track of the cost\n",
    "    t = 0                            # initializing the counter required for Adam update\n",
    "    seed = 10                        # For grading purposes, so that your \"random\" minibatches are the same as ours\n",
    "    \n",
    "    # Initialize parameters\n",
    "    parameters = initialize_parameters(layers_dims)\n",
    "\n",
    "    # Initialize the optimizer\n",
    "    if optimizer == \"gd\":\n",
    "        pass # no initialization required for gradient descent\n",
    "    elif optimizer == \"momentum\":\n",
    "        v = initialize_velocity(parameters)\n",
    "    elif optimizer == \"adam\":\n",
    "        v, s = initialize_adam(parameters)\n",
    "    \n",
    "    # Optimization loop\n",
    "    for i in range(num_epochs):\n",
    "        \n",
    "        # Define the random minibatches. We increment the seed to reshuffle differently the dataset after each epoch\n",
    "        seed = seed + 1\n",
    "        minibatches = random_mini_batches(X, Y, mini_batch_size, seed)\n",
    "\n",
    "        for minibatch in minibatches:\n",
    "\n",
    "            # Select a minibatch\n",
    "            (minibatch_X, minibatch_Y) = minibatch\n",
    "\n",
    "            # Forward propagation\n",
    "            a3, caches = forward_propagation(minibatch_X, parameters)\n",
    "\n",
    "            # Compute cost\n",
    "            cost = compute_cost(a3, minibatch_Y)\n",
    "\n",
    "            # Backward propagation\n",
    "            grads = backward_propagation(minibatch_X, minibatch_Y, caches)\n",
    "\n",
    "            # Update parameters\n",
    "            if optimizer == \"gd\":\n",
    "                parameters = update_parameters_with_gd(parameters, grads, learning_rate)\n",
    "            elif optimizer == \"momentum\":\n",
    "                parameters, v = update_parameters_with_momentum(parameters, grads, v, beta, learning_rate)\n",
    "            elif optimizer == \"adam\":\n",
    "                t = t + 1 # Adam counter\n",
    "                parameters, v, s = update_parameters_with_adam(parameters, grads, v, s,\n",
    "                                                               t, learning_rate, beta1, beta2,  epsilon)\n",
    "        \n",
    "        # Print the cost every 1000 epoch\n",
    "        if print_cost and i % 1000 == 0:\n",
    "            print (\"Cost after epoch %i: %f\" %(i, cost))\n",
    "        if print_cost and i % 100 == 0:\n",
    "            costs.append(cost)\n",
    "                \n",
    "    # plot the cost\n",
    "    plt.plot(costs)\n",
    "    plt.ylabel('cost')\n",
    "    plt.xlabel('epochs (per 100)')\n",
    "    plt.title(\"Learning rate = \" + str(learning_rate))\n",
    "    plt.show()\n",
    "\n",
    "    return parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You will now run this 3 layer neural network with each of the 3 optimization methods.\n",
    "\n",
    "### 5.1 - Mini-batch Gradient descent\n",
    "\n",
    "Run the following code to see how the model does with mini-batch gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.701832\n",
      "Cost after epoch 1000: 0.669851\n",
      "Cost after epoch 2000: 0.638018\n",
      "Cost after epoch 3000: 0.588729\n",
      "Cost after epoch 4000: 0.576679\n",
      "Cost after epoch 5000: 0.544973\n",
      "Cost after epoch 6000: 0.523694\n",
      "Cost after epoch 7000: 0.526341\n",
      "Cost after epoch 8000: 0.481660\n",
      "Cost after epoch 9000: 0.479216\n"
     ]
    },
    {
     "data": {
      "image/png": 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+sB+4CrjFQzEZ06P1Cwlg4ffP4FcXpbE+p4TZjyzn4SXbT2gfBWVV3PnyWrYV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\nk13kWGZq875SHvtkBwDrWyx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lw2M97e0Auji7Pu2z69M+uz5ts2vTPo9eH3tmaIwxptez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\nj2vydve1qH0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f3906b8a0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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KNZaWJdUyhwq1GZ5h9KTMptBjetUN1RFdT3tVI+OUfa5cKlWl1CpqOdevlXZ+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\nvNdWWAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390686e128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"gd\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Gradient Descent optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.2 - Mini-batch gradient descent with momentum\n",
    "\n",
    "Run the following code to see how the model does with momentum. Because this example is relatively simple, the gains from using momemtum are small; but for more complex problems you might see bigger gains."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.701854\n",
      "Cost after epoch 1000: 0.669920\n",
      "Cost after epoch 2000: 0.638121\n",
      "Cost after epoch 3000: 0.588832\n",
      "Cost after epoch 4000: 0.576763\n",
      "Cost after epoch 5000: 0.545053\n",
      "Cost after epoch 6000: 0.523772\n",
      "Cost after epoch 7000: 0.526427\n",
      "Cost after epoch 8000: 0.481915\n",
      "Cost after epoch 9000: 0.479377\n"
     ]
    },
    {
     "data": {
      "image/png": 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6s2n8YPogPli3nxl/X8QLX+8+pmsUHqri1pdW8M3Og/zhg43HHENNbR3PfbWb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\nyujEY0uG7XHZxCTqFN5elUV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390673dc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.796666666667\n"
     ]
    },
    {
     "data": {
      "image/png": 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QQNd8vVLH8VVoelM6q5Um/vLF3Lb86tjx45HAOZaG2VoJqLpeDwo5D6tk0Zvc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6Wu9JSAW+7OUclksMqVs43dYOLagpaGJIR6QVqelopsn8W+DnrmVq58kQ+fv6RndpnBC4vkSkGh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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f39067fa320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, beta = 0.9, optimizer = \"momentum\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Momentum optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.3 - Mini-batch with Adam mode\n",
    "\n",
    "Run the following code to see how the model does with Adam."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost after epoch 0: 0.689255\n",
      "Cost after epoch 1000: 0.150679\n",
      "Cost after epoch 2000: 0.134667\n",
      "Cost after epoch 3000: 0.143598\n",
      "Cost after epoch 4000: 0.150224\n",
      "Cost after epoch 5000: 0.142832\n",
      "Cost after epoch 6000: 0.131771\n",
      "Cost after epoch 7000: 0.121991\n",
      "Cost after epoch 8000: 0.119981\n",
      "Cost after epoch 9000: 0.135285\n"
     ]
    },
    {
     "data": {
      "image/png": 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61djvG7PX8v6CDby/YAPjp6/kzjMP5ePFeTwzdSVjju/BLSP7siG/mHvfX8LZ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\nLhHaSk4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390671bac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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HECiyOZPR8f33SO6GYQhzZxNMzyp8T2HZErqPsQmLpYXuwp90xggdMD1oVKsB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\nA6Guqc9qj9WYBNpFazpFm973SISRGhkJVMk4ElDe6rJ2rUSmHd8wBKp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rkJqgVbLVfune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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f390673d630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train 3-layer model\n",
    "layers_dims = [train_X.shape[0], 5, 2, 1]\n",
    "parameters = model(train_X, train_Y, layers_dims, optimizer = \"adam\")\n",
    "\n",
    "# Predict\n",
    "predictions = predict(train_X, train_Y, parameters)\n",
    "\n",
    "# Plot decision boundary\n",
    "plt.title(\"Model with Adam optimization\")\n",
    "axes = plt.gca()\n",
    "axes.set_xlim([-1.5,2.5])\n",
    "axes.set_ylim([-1,1.5])\n",
    "plot_decision_boundary(lambda x: predict_dec(parameters, x.T), train_X, train_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 5.4 - Summary\n",
    "\n",
    "<table> \n",
    "    <tr>\n",
    "        <td>\n",
    "        **optimization method**\n",
    "        </td>\n",
    "        <td>\n",
    "        **accuracy**\n",
    "        </td>\n",
    "        <td>\n",
    "        **cost shape**\n",
    "        </td>\n",
    "\n",
    "    </tr>\n",
    "        <td>\n",
    "        Gradient descent\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Momentum\n",
    "        </td>\n",
    "        <td>\n",
    "        79.7%\n",
    "        </td>\n",
    "        <td>\n",
    "        oscillations\n",
    "        </td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>\n",
    "        Adam\n",
    "        </td>\n",
    "        <td>\n",
    "        94%\n",
    "        </td>\n",
    "        <td>\n",
    "        smoother\n",
    "        </td>\n",
    "    </tr>\n",
    "</table> \n",
    "\n",
    "Momentum usually helps, but given the small learning rate and the simplistic dataset, its impact is almost negligeable. Also, the huge oscillations you see in the cost come from the fact that some minibatches are more difficult thans others for the optimization algorithm.\n",
    "\n",
    "Adam on the other hand, clearly outperforms mini-batch gradient descent and Momentum. If you run the model for more epochs on this simple dataset, all three methods will lead to very good results. However, you've seen that Adam converges a lot faster.\n",
    "\n",
    "Some advantages of Adam include:\n",
    "- Relatively low memory requirements (though higher than gradient descent and gradient descent with momentum) \n",
    "- Usually works well even with little tuning of hyperparameters (except $\\alpha$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**References**:\n",
    "\n",
    "- Adam paper: https://arxiv.org/pdf/1412.6980.pdf"
   ]
  }
 ],
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